Dual-phase-lag thermoelastic shock response of an inhomogeneous temperature-dependent lamina with nonlinear material properties

Abstract

This paper develops a dual-phase-lag thermoelastic model for a one-dimensional inhomogeneous lamina exposed to coupled thermal and mechanical shock loading. The formulation is built for a graded medium whose elastic, thermal, inertial and thermoelastic coupling coefficients depend simultaneously on the spatial coordinate and the local temperature increment. The dual-phase-lag heat law introduces two physically distinct delay times: the heat-flux lag and the temperature-gradient lag. This feature allows the model to describe delayed heat-flow response without forcing the thermal disturbance to behave as a purely diffusive process. The governing equations are derived from the nonlinear constitutive law, the equation of motion, the energy balance and the DPL heat-flux relation. Because the coefficients depend on temperature, the transformed problem is nonlinear and is treated through a Picard-type iterative procedure in the Laplace domain, followed by numerical inversion. Parametric results are presented for the effects of the heat-flux lag, the temperature-gradient lag, spatial inhomogeneity and temperature-dependent conductivity and stiffness. The results show that the lag ratio strongly controls the sharpness of the thermal wave front, while thermal stiffening can reduce displacement but increase local stress. The model provides a useful framework for graded laminae used in laser processing, microelectronic strips, thermal barrier layers and other structures subjected to fast transient heating.